The Music of the Spheres

He himself could hear the harmony of the Universe, and understood the music of the spheres, and the stars which move in concert with them, and which we cannot hear because of the limitations of our weak nature (Porphyry, Life of Pythagoras)

I love legends. The life of Pythagoras is riddled with them: from the discoverie of consonant intervals in music while walking past a forge to how give death to his disciple Hippasus throwing him overboard a ship after this one proved the existence of irrational numbers. My favorite is the one that heads this post: it is said that Pythagoras could hear the sound of the spheres, the harmony of the universe. No more no less.

Nowadays is accepted that Pythagoras could not deduce the mathematical rules of consonant intervals just weighting hammers. Not even is known if Hippasus (who paradoxically demonstrated the existence of irrationals thanks to the theorem of Pythagoras) was killed. Furthermore, it’s possible that Pythagoras suffered from tinnitus: a common dolence that provoques the perception of sound when no corresponding external sound is present. That, together with some dose of marketing, could explain why he listened to the evolution of the stars.

This post is a tribute to the things and people that inspire us. There are two great sources of inspiration in it:

• On the one hand, the work of Mark Lombardi, an american artist known for his abstract diagrammatic hand drawings, using curvy arcs and edges to capture global frauds perpetrated by politicians during 1980. The Modern Art Museum in NYC collected many of his works. Lombardi called his diagrams Narrative Structures, where this type of graph was often used to display social network analysis. I have been introduced to Lombardi’s work through a recent scientific collaboration with Alon Friedman, Professor at the School of Information in the University of South Florida.
• On the other hand is Nina Simone, that accompanies me very often while I run, while I cook or while I work. She is a fundamental part of the soundtrack of my life. The sun around which the planets revolve is the one that appears on the cover of his album Here Comes the Sun:

If you take a look to the code you will find that all begins with a initial circular orbit where I place some of the planets (you can choose how many planets draw in total with the parameter nu_nodes). After that, I pick random planet from which will start a new orbit where I will place some other planets and so on (here is when I imitate some of the Lombardi’s arrangements for his structures). I expand each new orbit away from the sun, so that space gets a bit darker the farther we get from it. Apart from the parameter nu_nodes, you can also play with max_ratio (how big is the sun) and nu_branches (number of orbits) but you will find other places to tweak if you dive into de code. Here you have some other examples of what you can get:

Each one chooses which legends to believe and which not. I do believe that Pythagoras could listen to the music of the spheres: we must not forget that he already gave proof of having a superhuman ability discovering the most famous theorem in history.